Scale-free structural organization of oxygen interstitials in La(2)CuO(4+y).

It is well known that the microstructures of the transition-metal oxides, including the high-transition-temperature (high-T(c)) copper oxide superconductors, are complex. This is particularly so when there are oxygen interstitials or vacancies, which influence the bulk properties. For example, the oxygen interstitials in the spacer layers separating the superconducting CuO(2) planes undergo ordering phenomena in Sr(2)O(1+y)CuO(2) (ref. 9), YBa(2)Cu(3)O(6+y) (ref. 10) and La(2)CuO(4+y) (refs 11-15) that induce enhancements in the transition temperatures with no changes in hole concentrations. It is also known that complex systems often have a scale-invariant structural organization, but hitherto none had been found in high-T(c) materials. Here we report that the ordering of oxygen interstitials in the La(2)O(2+y) spacer layers of La(2)CuO(4+y) high-T(c) superconductors is characterized by a fractal distribution up to a maximum limiting size of 400 mum. Intriguingly, these fractal distributions of dopants seem to enhance superconductivity at high temperature.